Elez was born in Split and started to play football in the mid-1990s at local club Omladinac, which is now known as NK Omladinac. In June 1994, he was spotted by Hajduk Split, and started his professional career by joining the club in March 1994. He played for Hajduk until 1999, and then he moved in other club "Mosor", he play for second team. After two seasons he moved in first team. That year Mosor played in Croatia second league and Elez was the best young player in the non-professional league.
After two seasons with Mosor, he left and signed with NK Uskok and he played two seasons there, with some success. In the summer 2005 Elez left NK USKOK and started to play for NK Slaven Belupo in the Croatian first division, where he remained for two seasons before joining Zadar.